Abstract

Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations in C[0,T]. Finally, we expose a genuine example to support the effectiveness of our results.

Details

Title
Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
Author
Vahid, Parvaneh 1   VIAFID ORCID Logo  ; Khorshidi Maryam 2 ; De La Sen Manuel 3 ; Işık Hüseyin 4 ; Mursaleen Mohammad 5 

1  Islamic Azad University, Department of Mathematics, Gilan-E-Gharb Branch, Gilan-E-Gharb, Iran 
2  Firouzabad Institute of Higher Education, Department of Mathematics, Firouzabad, Iran 
3  University of The Basque Country, Institute of Research and Development of Processes, Leioa, Spain (GRID:grid.11480.3c) (ISNI:0000000121671098) 
4  Muş Alparslan University, Department of Mathematics, Muş, Turkey (GRID:grid.449204.f) 
5  China Medical University (Taiwan), Department of Medical Research, China Medical University Hospital, Taichung, Taiwan (GRID:grid.254145.3) (ISNI:0000 0001 0083 6092); Asia University, Department of Computer Science and Information Engineering, Taichung, Taiwan (GRID:grid.252470.6) (ISNI:0000 0000 9263 9645); Aligarh Muslim University, Department of Mathematics, Aligarh, India (GRID:grid.411340.3) (ISNI:0000 0004 1937 0765) 
Publication year
2020
Publication date
Dec 2020
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-020-02703-z
ProQuest document ID
2407212237
Copyright
© The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.